Electrostrictive Corrections to the Pseudo One-Dimensional Ising Model of Ferroelectrics

A pseudo-two-dimensional Ising model of ferroelectrics

“…Through this model, which could be applied to biological lipid bilayers [25][26][27][28], we study the paraand ferroelectric behaviours of different thermodynamic properties for different ratios of interaction constants and different values of electric field, by using a transfer matrix method for the intra-ladder interactions and the MF approximation for the inter-ladder interactions. In a particular case of our model, in which the interactions between two layers (planes) are taken to be zero, our results reproduce entirely those obtained previously for a pseudo-onedimensional Ising model, which explains well the experimental data for the thermodynamic properties of 1D ferroelectrics such as CsD 2 PO 4 (d-CDP) [24].…”

“…Following [24] performing a Legendre transformation on g 0 (k, ξ ), we obtain the Helmholtz free energy for the simple Ising ladder as f 0 (k, p). If the inter-ladder interactions are treated by an MF approximation, then the internal energy term of the average polarization, −J y p 2 is added to the free energy.…”

“…where is the elastic constant, ξ is the strain and v is the volume of a molecular unit. Based on the assumption above, the coupling between the polarization and the strain is taken into the inter-ladder interaction constant as the following expansion [24]:…”

“…Thus, the orthorhombic compound vanadyl pyrophosphate (VO) 2 P 2 O 7 clearly shows a ladder configuration of spin- 1 2 V 4+ ions in its crystal lattice. Also, some years ago, many theories based upon the pseudo-onedimensional (1D) Ising model were applied to explain the thermodynamic properties of the 1D ferroelectrics such as CsH 2 PO 4 (CDP), PbHPO 4 (PMP) and their deuterated analogues d-CDP and d-PMP ( [18][19][20][21][22][23][24] and references therein).…”

Ab initiostudy of the one-dimensional H-bonded ferroelectricCsH2PO4

“…From the theoretical side, a common approach was to use the quasi-1D Ising model with intrachain and interchain couplings between pseudospins, including also the interaction with the external electric field [18,[23][24][25][26]. The interchain interaction is much smaller than the intrachain counterpart, and is treated by means of a mean-field theory.…”